Algebra Chapter on Functions and Patterns

Linear Functions and Relations

• Linear function: A fundamental concept represented as a straight line, crucial for advanced mathematics.
• Nonlinear: Any function that does not conform to linear characteristics.
• Function: A relationship where one quantity changes in response to another.

Patterns and Types

• Patterns: Can be geometric designs or sequences (algebraic or numeric) with repeating aspects, such as numeric patterns (e.g., 4, 7, 10, 13) involving consistent addition.
• Algebraic pattern: Involves numbers and variables arranged in a specific sequence.

Mathematical Operations and Relationships

• Fact family: A group of numbers connected through various mathematical operations, such as addition and subtraction.
• Algebraic expression: A combination of variables and constants that lacks a relational symbol (e.g., 5y + 8).
• Coefficient: The number that precedes a variable in an expression, indicating the quantity of that variable.

Types of Algebraic Expressions

• Monomial: An algebraic expression consisting of a single term.
• Binomial: An expression with two terms (e.g., 2ab - cd).
• Trinomial: An algebraic expression containing three terms.
• Polynomial: Represents expressions with more than one term.

Graphical Representations

• Graph: Visual representation illustrating numerical relationships.
• Table: An organized listing of values typically arranged in rows and columns to show functions and relationships.
• Pictorial graph: The most tangible representation, transitioning from real objects to symbolic forms.
• Bar Graph: Displays data using horizontal or vertical bars.
• Line Graphs: Illustrates relationships among two or more variables through data points.
• Pie Chart: Visualizes relationships as parts of a whole, typically used for percentages.

Learning Progressions in Mathematics

• Concrete models: Effective tools for younger students (e.g., Kindergarten) to explore patterns through hands-on attributes (e.g., patterns like AB, AAB).
• Transition in learning: By third grade, students progress to using tables and graphs to represent relationships between two variables.

Mathematical Equations and Inequalities

• Equations: Statements asserting the equivalence of two expressions, marked by an equals sign (e.g., (7 + 2 = 10 - 1)).
• Algebraic inequality: Expresses a relationship showing greater or lesser value between variables and constants (e.g., (2x + 8 > 24)).